Finding Electric Field at Rectangle Center: A Problem

[spoonthrower]

Here is the problem i am stuck on: There are 4 charges arranged in a rectangle pictured with side lengths .03m and .05m. The top 2 charges are negative and the bottom 2 charges are positive. All 4 charges have the same magnitude of 8.60*10^-12 C. Find the magnitude of the electric field at the center of the rectangle as pictured:

1 2
-***-
* *
* *
* *
* *
* *
+***+
3 4

So first i found the radius to each charge which is the same for all the charges. so the radius is the square root of (.015m^2+.025^2) = .0292 m
So i know that E1=E2=E3=E4 since the radius is the same for all the charges. So E=kq/(r^2)=8.99*10^9(8.6*10^-12)/(.029^2)=91.9. The Electric field is doubled though for the top 2 charges because the positive electric field points away from itself and the negative electric field points toward itself so i know that this combined electric field is 2*91.9 = 184. I know this is right because i got this part of the question right. Now to find the electric field at the center of the rectangle, i would think to use the pythagorean theorom and say Enet= square root of (184^2+184^2)= 260. However, the CPU tells me this is wrong. Please help me out. Thanks.

 

[Nate810]

The electric field at the center of the rectangle is not just the sum of the two electric fields from charges 1 and 3. You need to take into account the electric fields from charges 2 and 4 as well. The electric field at the center of the rectangle is the vector sum of the four electric fields, which can be found using the superposition principle (https://en.wikipedia.org/wiki/Superposition_principle).

 

[kyle8921]

I would first commend you for your efforts in solving this problem. It is clear that you have a good understanding of the concept of electric fields and how they are affected by the arrangement of charges.

To solve for the electric field at the center of the rectangle, we need to take into account the vector nature of electric fields. The electric field at the center of the rectangle will be the sum of the electric fields from all four charges, taking into account their direction.

Using the formula for electric field, E = kq/r^2, we can calculate the electric field from each charge individually. However, we need to consider the direction of the electric field for each charge. For the top two charges, the electric field will be pointing away from the center, while for the bottom two charges, the electric field will be pointing towards the center.

Therefore, the electric field at the center of the rectangle will be the vector sum of the individual electric fields from each charge. This can be calculated using vector addition, taking into account the direction and magnitude of each electric field.

I would suggest breaking down the problem into smaller components and using vector addition to calculate the final electric field at the center of the rectangle. This will give you a more accurate answer than simply using the Pythagorean theorem.

I hope this helps and good luck with your problem-solving!